Question

two pipes A and B can separately fill in 15 and 10 minutes respectively and a waste pipe c can carry off 7litres per minute.if all The pipes are opened when The cistern is full,it is emptied in 2 hours .how many litres does the cistern hold ?
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Answer 1

Gɪᴠᴇɴ :-

• A pipe alone can fill the cistern in = 15 minutes.
• B pipe alone can fill the cistern in = 10 minutes.
• Waste Pipe C carry off water out = 7 Litre / Min.
• If all Three opened Cistern is emptied in = 2 Hours.

Tᴏ Fɪɴᴅ :-

• Total Capacity of Cistern ?

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That C Empty The full Cistern in x Min.

Than,

→ in One Min. A Alone Fill = (1/15)

→ in one Min. B Alone Fill = (1/10)

→ in one Min. C alone Empty = (1/x)

Now, we have given that, when All three Opened full cistern was Emptied in 2 Hours .(120Min.)

So, we can say That,

→ (1/x) - [1/15 + 1/10] = 1/120

→ 1/x = (1/120) + (1/15) + (1/10)

→ 1/x = (1 + 8 + 12)/120

→ 1/x = (21/120)

→ x = (120/21) Min.

Therefore, we can conclude That, C alone Can Empty The full Cistern in (120/21) Min.

And, we have Given That,

→ C carry off water out = 7 Litre / Min.

So ,

→ in (120/21) Min. C carry off water out = (120/21) * 7 = 40 Litre (Ans.)

Hence, Capacity of Cistern is 40 Litre.